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1. Determination of Activation Energy for Dehydroxylation of Illite The kinetics of chemical reactions are commonly expressed as da = k f (a ) , dt (1) æ -Ea ö k = Aexp ç ÷, è RT ø (2) where is the reacted fraction of a substance (0 ≤ ≤ 1; = 1 if the entire substance is reacted), t is reaction time, k is reaction rate, and f( is a kinetic (rate-limited) function determined by the reaction mechanism (this can be a first- or second-order reaction, one-, two- or three-dimensional diffusion, two- or three-dimensional phase boundary, or two-, three-, or ndimensional nucleation [e.g., Koga, 1997]. The relationship between reaction rate k and temperature, as expressed by the Arrhenius equation, is where A is a constant (pre-exponential term), Ea is the activation energy necessary for a reaction to occur, R is the gas constant (8.31447 J K-1 mol-1), and T is temperature (K). The Friedman analysis (or differential isoconversional method) is widely used to determine Ea independent of the kinetic function in experiments carried out at different heating rates. From Eqs. 1 and 2, da E 1 (3) = - a + ln [ Af (a )] . dt RT At any fixed , the logarithmic term on the right side of Eq. 3 is a constant, so the logarithm of the conversion rate d/dt over the inverse of temperature 1/T describes a straight line with a ln slope of –Ea/R. In this way, Ea can be determined independently from the selection of the kinetic function. Thermogravimetric profiles at heating rates of 5, 10, and 20 °C min-1 were obtained using a Netzsch STA 449 C Jupiter balance. Using the kinetic software Netzsch Thermokinetics with Ea values constrained by Friedman analysis on the basis of Eq. 3, the most appropriate kinetic function and values of A and Ea can be determined and their validity assessed by F-test statistical analysis. The detail of this sequential procedure was described by Hirono and Tanikawa [2011]. A two-step reaction was considered in our kinetic analysis, because dehydroxylation of illite (from the Tokaji Mountains of northeastern Hungary) [Gualtieri and Ferrari, 2006] and illite– muscovite (from the Rochester Shale, New York state, USA) [Hirono and Tanikawa, 2011] showed such a reaction. The two-step reaction mechanism is expressed as æ -E ö da1st (4) = A1st exp ç a_1st ÷ f (a1st ) , dt è RT ø æ -Ea _ 2nd ö æ -Ea _1st ö da 2nd (5) = A2nd expç ÷ f (a 2nd ) - A1st expç ÷ f (a1st ), dt è RT ø è RT ø where 1st is the reacted fraction of an intermediate product at the first step (0 ≤ 1st ≤ 1) and A1st, Ea_1st, and f(1st are the pre-exponential term, activation energy, and kinetic function, respectively, for the first-step reaction; and 2nd is the reacted fraction of the final product after the second step (0 ≤ 2nd ≤ 1), and A2nd, Ea_2nd, and f(2nd are the pre-exponential term, activation energy, and kinetic function, respectively, for the second-step reaction. Using Netzsch Thermokinetics software, including F-test statistical analysis, the most appropriate kinetic 1 function and values of A and Ea parameters can be determined. The details of this analysis have also been documented by Hirono and Tanikawa [2011]. The best-fitted function of both first- and second-step reactions, by this analysis, was threedimensional diffusion. Values of Ea_1st and Ea_2nd determined are shown in table A1. There are some problems that remain to be solved before we can meaningfully consider the results of our rotary shear experiments, kinetic analyses, and the feedback processes we considered in terms of natural faults and earthquakes. 1) The temperature reached by the highly damaged sample after 15 m of frictional slip at 1.5 MPa normal stress (Figure 1a) was higher than 300 °C, indicating that the dehydroxylation reaction had already started. In fact, the second-step weight loss of the sample (3.72 wt%) was 0.19 wt% lower than that of the initial sample (3.91 wt%), indicating that approximately 5% of the reaction had already occurred. Thus, there is uncertainty about the accuracy of the Ea_2nd value determined under experimental conditions with high frictional heat such as ours. 2) The Ea_2nd value of 142.3 kJ mol-1 for our initial illite sample was lower than the 230 kJ mol-1 value obtained for the illite of Gualtieri and Ferrari [2006] and that of 181.8 kJ mol-1 for the illite–muscovite of Hirono and Tanikawa [2011]. These discrepancies may reflect different polytypes and interlayer charges of the illite samples used, but this needs to be clarified. 3) The maximum frictional energy density attained in our rotary shear experiments was 17.65 MJ m-3 (for 15 m displacement at 1.5 MPa normal stress). This value corresponds to a fault slip of only 4 cm at 1.5 km depth, assuming a slip zone that is 1 cm thick, a frictional coefficient of 0.2, hydrostatic confining stress (normal stress on the slip zone = overburden stress), and not accounting for thermal pressurization (other parameters are shown in table A2). Thus, natural fault slip is accompanied by much higher frictional energy density in the slip zone, probably inducing a large decrease of Ea and causing dramatic coseismic mechanochemical effects. However, it is difficult to demonstrate such high frictional energy density with our rotary shear apparatus because of the likelihood of leakage of the sample and the high temperatures caused by friction. 2 2. Dynamic Numerical Analysis of Earthquake Slip According to heat balance, the temperature (T) at a distance x from the centre of the slip zone is expressed in terms of the balance at time t as ¶T ¶ æ ¶T ö (6) ( rc)e = Ah - çè le ÷ø , ¶t ¶x ¶x where Ah is heat production rate, (c)e is equivalent specific heat capacity, is density, c is specific heat, and λe is equivalent thermal conductivity. The equivalent specific heat capacity and thermal conductivity are described respectively as (7) ( rc)e = (1- f ) rr cr + fr f cf and (8) le = (1- f ) lr + fl f , where is porosity; r, cr, and r are respectively the density, specific heat capacity, and thermal conductivity for the grain matrix (illite); and f, cf, and f are the same for pore fluid (water). Thermal conductivity was calculated from specific heat and thermal diffusivity, , as = c. (9) Eq. 8 corresponds to an arithmetic mean that represents the upper limit of thermal conductivity for porous media [Abdulagatova et al., 2009]. A fault model in which the slip zone is localized within a finite thickness, w, is considered here. The strain rate is assumed to be constant across the thickness of the fault, according to Mair and Marone [2000] and Fialko [2004]. With the assumptions that total frictional work is converted to heat and that energy is consumed by chemical reaction, the rate of heat production is expressed as ù ¶é d v ¶E Ah = êm ( Pc - Pf ) - Ec ú = m ( Pc - Pf ) - c (x<|w/2|) û ¶t ë w w ¶t ¶E (x|w/2|), (10) Ah = - c ¶t where is the coefficient of friction, Pc is confining pressure, Pf is pore-fluid pressure, d is slip displacement, is slip velocity, and Ec is the energy taken up by the endothermic reaction. Ec is related to chemical kinetics as (11) Ec = arh H , where is the reacted fraction, h is the density of the reactant (here hydrated mineral, illite, =r), and H is the heat per unit mass of an endothermic reaction, which corresponds to its enthalpy. The enthalpy is negative (H < 0) for an exothermic reaction. The fluid diffusion equation is ¶ Pf ¶ æ k ¶ Pf ö ¶T (12) Ss = ç ÷ + f (a f - a r ) + Qdeh , ¶t ¶ x è h ¶ x ø ¶t where Ss is the specific storage, f is the coefficient of thermal expansion of water, r is the coefficient of thermal expansion of the grain matrix, Qdeh is the pore pressure generated by the dehydroxylation reaction, k is permeability, and is fluid viscosity. The viscosity of water is expressed as a function of temperature as [Fontaine et al., 2001]: h = 2.414 ´10 ´ 10 -5 247.8 T +133 . (13) 3 Assuming that in the reaction 1 mol of hydrated mineral (illite) produces n mol of water and 1 mol of dehydrated mineral, ¶f æ n×Vf Vdeh ö (14) Qdeh = h ç +1÷, ¶ t è Vh Vh ø where h is the volume fraction of the hydrated mineral, Vf /Vh is the molecular volume ratio of the hydrated mineral to water, and Vdeh/Vh is the molecular volume ratio of hydrated to dehydrated minerals [Tanikawa et al., 2009]. The chemical conversion rate is related to the volume fraction rate as ¶a 1 ¶fh , (15) =¶t fh0 ¶ t where /t is the same as in Eq. 1 and h0 is the initial volume fraction of the hydrated mineral. Combining Eqs. 14 and 15, Qdeh is expressed as ¶a æ n × Vf Vdeh ö (16) Qdeh = -f h0 + 1÷ . ç¶t è Vh Vh ø The molecular volume ratio, n∙Vf/Vh, in Eq. 16 was not evaluated directly because the number of moles of water dehydrated from hydrated mineral, n, and the molecular volume of hydrated mineral, Vh, were not certain. However, this term is expressed by the weight mass ratio in chemical reactions as n×Vf 1 wf rh , (17) = Vh M f wh r f where Mf is the molar mass of water and wf/wh is the mass ratio of hydrated mineral to water for the dehydration reaction. The ratio wf/wh is evaluated from the average weight loss during heat treatment of the illite sample by TG. The dehydration volume ratio, Vdeh/Vh, is evaluated from the weight loss by thermal treatment using Vdeh wdeh rh , (18) = Vh wh rdeh where wdeh/wh is the mass ratio of hydrated to dehydrated minerals and deh is the density of dehydrated mineral. We assumed that the slip zone and its surroundings are composed of the same illite; that is, the hydraulic, thermal, and chemical kinetic properties of the host rock outside the slip zone were the same as those of the slip zone. In addition, the initial illite and dehydroxylated illite samples were assigned the same physical properties (h = deh). For the fault gouge simulation, the dependency of effective vertical pressure, Pe, on porosity is approximated as [Wibberley and Shimamoto, 2005] (19) f = 0.056exp(0.00297Pe ). For illite-rich clay, the dependency of effective vertical pressure on the void ratio, evoid, is approximated as [Djeran-Maigre et al., 1998] (20) evoid = 0.66 - 0.32logPe. The void ratio can be converted to porosity using 1 . (21) f= evoid +1 The specific storage, Ss, in Eq. 12 is calculated from the porosity and fluid compressibility as [Tanikawa et al., 2008] 4 1 df (22) + bf , 1- f dPe where is the compressibility of water. Hydraulic diffusivity, Dh, was calculated as k . (23) Dh = hSs For reference, the change of Dh with Pe from 2 to 100 MPa at temperatures of 300 and 1300 K is shown in figure A3. By using the finite difference method (time increment of 0.001 s and grid size of 0.5 mm), these equations (Eqs. 4–6, 11–23) were simultaneously solved with assumptions of 100 wt% illite composition and hydrostatic confining stress (normal stress acting on the slip zone = overburden stress), and the changes with time of pore-fluid pressure, shear stress, temperature, and reacted fraction at position x were obtained. Values of the parameters required for this simulation are summarized in table A2. Since Pf reaches Pc, we assumed that temperature remains constant and energy taken up by the dehydroxylation reaction is ignored. The resultant profiles of Pf, shear stress, 2nd, T, and hydraulic diffusivity with slip displacement are discussed in the main text (Figure 3). Additionally, we note here the following. 1) Although two damaged cases of 1.5 and 6.0 km depths were applied using only Ea = 97.0 mol-1, the frictional energy densities at such depths can immediately reach 17.65 MJ m-3, thus allowing Ea = 97.0 kJ mol-1 just after the start of slip. 2) Hydraulic diffusivity for the fault gouge of Wibberley and Shimamoto [2005] is lower than that of the illite-rich clay of Djeran-Maigre et al. [1998] for Pe < ~20 MPa (figure A3), which strongly affects the intense pressurization of the interstitial fluids and H2O released from the illite sample in the fault gouge of Wibberley and Shimamoto [2005] (Figure 3a). 2) Changes of pore-fluid pressure in the fault gouge of Wibberley and Shimamoto [2005] showed a two-step increase (Figure 3a), the first corresponding to pressurization of interstitial fluid and the second to release of H2O from the illite sample (Figure 3a, e). 4) After Pf reached Pc, the reacted fractions increased with time because of the assumed constant temperature (Figure 3e, g). However, in natural faults, the heat remaining after slip could lengthen the time of reaction [e.g., Hirono et al., 2008; Hamada et al., 2009]. 5) The temperature at which dry illite melts (Figure 3g, h) was assumed to be approximately 1150 °C [Balkyavichus et al., 2003], but wet conditions in a natural setting may lower that temperature. Thus, melt lubrication may take effect dominantly under the conditions of higher shear stress at greater depths. 6) Although only 1-cm-thick slip zone was applied for our simulation, not only permeability and mechanochemical effect but also the thickness strongly affects numerical results [e.g., Hirono and Tanikawa, 2011]. 7) The pressure dependency of kinetic parameters (Ea) was not considered in our simulation. In addition, faster heating during earthquake slip may require different kinetic functions and parameters than those for heating at 5–20 °C min–1. Future work should attempt to determine these parameters under high-pressure and at fast rates of heating to provide a more realistic evaluation of fault behavior. Ss = 5 References Abdulagatova, Z., I. M. Abdulagatov, and V. N. Emirov (2009), Effect of temperature and pressure on the thermal conductivity of sandstone, Int. J. Rock Mech. Min. Sci., 46, 1055– 1071. Balkyavichus, V., Ch. Valyukyavichus, A. Shpokauskas, A. Laukaitis, and F. Pyatrikaitis (2003), Sinterability of low-melting illite-bearing clays, Glass and Ceramics, 60, 179–182. Bayer, G. (1973), Thermal expansion anisotropy of oxide compounds, Proc. Br. Ceram. Soc., 22, 39–53. Djeran-Maigre, I., D. Tessier, D. Grunberger, B. Velde, and G. Vasseu (1998), Evolution of microstructures and of macroscopic properties of some clays during experimental compaction, Mar. Pet. Geol., 15, 109–128. Fialko, Y. (2004), Temperature fields generated by the elastodynamic propagation of shear cracks in the Earth, J. Geophys. Res., 109, B01303, doi:10.1029/2003JB002497. Fine, R. A., and F. J. Millero (1973), Compressibility of water as a function of temperature and pressure, J. Chem. Phys., 59, 5529–5536. Fontaine, F. J., M. Rabinowicz, and J. Boulegue (2001), Permeability changes due to mineral diagenesis in fractured crust; Implications for hydrothermal circulation at mid-ocean ridges, Earth Planet. Sci. Lett., 184, 407–425. Gualtieri, A. F., and S. Ferrari (2006), Kinetics of illite dehydroxylation, Phys. Chem. Minerals, 33, 490–501, doi:10.1007/s00269-006-0092-z. Hamada, Y., T. Hirono, W. Tanikawa, W. Soh, and S.-R. Song (2009), Energy taken up by coseismic chemical reactions during a large earthquake: An example from the 1999 Taiwan Chi-Chi earthquake, Geophys. Res. Lett., 36, L06301, doi:10.1029/2008GL036772. Hirono, T. et al. (2008), Clay mineral reactions caused by frictional heating during an earthquake: An example from the Taiwan Chelungpu fault, Geophys. Res. Lett., 35, L16303, doi:10.1029/2008GL034476. Hirono, T., and W. Tanikawa (2011), Implications of the thermal properties and kinetic parameters of dehydroxylation of mica minerals for fault weakening, frictional heating, and earthquake energetics, Earth Planet. Sci. Lett., 307, 161–172, doi:10.1016/j.epsl.2011.04.042. Horváth, E., R. L. Frost, É. Makóc, J. Kristóf, and T. Cseh (2003), Thermal treatment of mechanochemically activated kaolinite, Thermochim. Acta, 404, 227–234, doi:10.1016/S0040-6031(03)00184-9. Koga, N. (1997), Physico-geometric kinetics of solid-state reactions by thermal analyses, J. Therm. Anal., 49, 45–56. Mair, K., and C. Marone (2000), Shear heating in granular layers, Pure Appl. Geophys., 157, 1847–1866. Mizoguchi, K., T. Hirose, T. Shimamoto, and E. Fukuyama (2009), High-velocity frictional behavior and microstructure evolution of fault gouge obtained from Nojima fault, southwest Japan, Tectonophysics, 471, 285–296, doi:10.1016/j.tecto.2009.02.033. 6 Tanikawa, W., M. Sakaguchi, T. Hirono, W. Lin, W. Soh, and S. Song (2009), Transport properties and dynamic processes in a fault zone from samples recovered from TCDP Hole B of the Taiwan Chelungpu Fault Drilling Project, Geochem. Geophys. Geosyst., 10, Q04013, doi:10.1029/2008GC002269. Tanikawa, W., T. Shimamoto, S.-K. Wey, C.-W. Lin, and W.-C. Lai (2008), Stratigraphic variation of transport properties and overpressure development in the Western Foothills, Taiwan, J. Geophys. Res., 113, B12403, doi:10.1029/2008JB005647. Vizcayno, C., R. Castelló, I. Ranz, and B. Calvo (2005), Some physico-chemical alterations caused by mechanochemical treatments in kaolinites of different structural order, Thermochim. Acta, 428, 173–183, doi:10.1016/j.tca.2004.11.012. Wibberley, C. A., and T. Shimamoto (2005), Earthquake slip weakening and asperities explained by thermal pressurization, Nature, 436, 689–692, doi:10.1038/nature03901. Yang, H., W. Yang, Y. Hu, C. Du, and A. Tang (2005), Effect of mechanochemical processing on illite particles, Part. Part. Sysr. Charact., 22, 207–211, doi:10.1002/ppsc.200500953. 7